US2 and MT200 cross the flat northern part of the state. US2 arond the south side of the park is one of the lowest passes over the Rockies. Years ago I camped at a COE campground near Wolf Point, and a map search should turn a few other options.
In the 2000s I chose to stay on I94 to Miles City, motel it there, and then take a 'diagonal' from Billings to St Marys. That was a full day of fuel efficient sub-freeway speeds driving. In part I chose that because I had limited information on my laptop MS Streets-n-trips about lodging options further north.
The I94/90 route is longer, and has more passes, but is closer to towns, camping and other lodging options, and other traveler facilities. It passes, for example the north gateways to Yellowstone.